I had wanted to do something for the 5th anniversary of the K-ON! anime, but didn't manage to finish it in time. I put a huge amount of effort into this, so I hope it was worth something.
Edit: (More info) The song is, of course, Houkago Tea Time. I chose it because the song seemed a little unrecognized, so to speak, and of course the AMV is about the band of the same name of the song. I also believe that the lyrics are related to the song; I certainly don't understand most of it but I do know meanings of certain lines like "Itsumademo Tea Time", etc.
I used Windows Live Movie Maker to do the video editing. I probably would have finished sooner if the program had not crashed on me every other minute or so.
I have some regrets in some of the content selection in this video, especially a bit at the end that I had saved but forgot to add. Nonetheless I hope you enjoy.
A more detailed blog post about the AMV is available here.
UPDATE: As of 21 May 2016, this video is down due to a copyright strike.